Trojan Virus?

My firewall keeps telling me about attempts to access my computer by a trojan horse. I have updated and run my Virus Checker several times and it doesn't find any problems. I even reformatted and reinstalled everything, but it still doesn't seem cured.

Yesterday, a couple of wierd things happened which have left me quite worried. The 'X' close program in the top right of all my windows turned to a white square with a black lightbulb on. Then the shortcuts on my desktop wouldn't work when clicked- they said they couldn't find their targets. Shutting down solved both these problems but I am concerned in case there is a virus causing them.